Vintage factor analysis is one important type of factor analysis that aims to
first find a low-dimensional representation of the original data, and then to
seek a rotation such that the rotated low-dimensional representation is
scientifically meaningful. Perhaps the most widely used vintage factor analysis
is the Principal Component Analysis (PCA) followed by the varimax rotation.
Despite its popularity, little theoretical guarantee can be provided mainly
because varimax rotation requires to solve a non-convex optimization over the
set of orthogonal matrices.
In this paper, we propose a deflation varimax procedure that solves each row
of an orthogonal matrix sequentially. In addition to its net computational gain
and flexibility, we are able to fully establish theoretical guarantees for the
proposed procedure in a broad context.
Adopting this new varimax approach as the second step after PCA, we further
analyze this two step procedure under a general class of factor models. Our
results show that it estimates the factor loading matrix in the optimal rate
when the signal-to-noise-ratio (SNR) is moderate or large. In the low SNR
regime, we offer possible improvement over using PCA and the deflation
procedure when the additive noise under the factor model is structured. The
modified procedure is shown to be optimal in all SNR regimes. Our theory is
valid for finite sample and allows the number of the latent factors to grow
with the sample size as well as the ambient dimension to grow with, or even
exceed, the sample size.
Extensive simulation and real data analysis further corroborate our
theoretical findings.

本文介绍了古董因子分析的一个重要类型 —— 主成分分析（PCA）和 varimax 旋转后的方差极大化旋转。通过将 PCA 与新的 deflation varimax 方法相结合，并使用一般类别的因子模型进行分析，我们发现它在中等或高信噪比条件下以最佳速率估计因子载荷矩阵，在低信噪比条件下当因子模型中的加性噪声具有结构时，改进的方法优于使用 PCA 和 deflation 程序。在有限样本条件下，理论有效且允许潜在因子的数量随样本量的增长而增长，同时允许环境维度随着样本量的增长甚至超过样本量。我们的理论结果得到了广泛的模拟和实际数据分析的验证。

基于通货紧缩变量旋转因子分析的最优模型

Optimal vintage factor analysis with deflation varimax

Among steganalysis techniques, detection against motion vector (MV)
domain-based video steganography in High Efficiency Video Coding (HEVC)
standard remains a hot and challenging issue. For the purpose of improving the
detection performance, this paper proposes a steganalysis feature based on the
optimality of predicted MVs with a dimension of one. Firstly, we point out that
the motion vector prediction (MVP) of the prediction unit (PU) encoded using
the Advanced Motion Vector Prediction (AMVP) technique satisfies the local
optimality in the cover video. Secondly, we analyze that in HEVC video, message
embedding either using MVP index or motion vector differences (MVD) may destroy
the above optimality of MVP. And then, we define the optimal rate of MVP in
HEVC video as a steganalysis feature. Finally, we conduct steganalysis
detection experiments on two general datasets for three popular steganography
methods and compare the performance with four state-of-the-art steganalysis
methods. The experimental results show that the proposed optimal rate of MVP
for all cover videos is 100\%, while the optimal rate of MVP for all stego
videos is less than 100\%. Therefore, the proposed steganography scheme can
accurately distinguish between cover videos and stego videos, and it is
efficiently applied to practical scenarios with no model training and low
computational complexity.

基于高效视频编码中运动矢量优化的隐写分析特征，本文提出一种能够准确识别覆盖视频和隐写视频的隐写方案，并且在无需模型训练和低计算复杂度的实际场景中表现高效。